INTERMEDIATE ALGEBRA OF TRANSITIONS IN MICROPROGRAM FINAL-STATE MACHINE

Abstract

The problem of formalization of representation of final-state machine, where the part of automaton transition is realized in noncanonicalway, is solved. A new approach for organization of the function of transitions of the final-state machine is proposed. According toit the function of transitions is represented as a family of partial functions, each of which is defined only on the part of the domain of thefunction of transitions, and corresponds to a subset of the automaton transitions. According to the proposed approach the traditional representation of the final-state machine as a polybasic algebra is changed. First, the mutual independence of the function of transitions and function of outputs that form the signature of algebra, allows us to consider them separately from each other. This way leads to presentation of the final-state machine as two algebras: the algebra of transitions whose signature contains only the function of transitions and algebra of outputs whose signature contains only the function of outputs. Second, the representation of the function of transitions in the form of a set of partial functions leads to the replacement of the algebra of transitions by the set of subalgebras of transitions, a signature of each of which is formed by partial function of transitions.The example of the final-state machine with a counter shows that the law of transformation of codes of states within a certain subset oftransitions can be set by an algebraic function (operation of transitions) using scalar interpretation of codes of states of the structural finalstatemachine. The representation of scalar interpretation of codes of states and the operation of transitions as so-called intermediate algebraof transitions isomorphic to both according subalgebras of transitions of the abstract and equivalent structural final-state machines is proposed.